LONDON—Britain’s upper house of parliament on Tuesday inflicted another embarrassing defeat on Prime Minister Theresa May’s government on Tuesday, challenging her plan to leave the European Union’s single market after Brexit.

May, who has struggled to unite the government behind her vision of Brexit, has said Britain will also leave the European Union’s single market and customs union after it quits the bloc next March.

That stance has widened divisions not only within her own Conservative Party but also across both houses of parliament, which like Britons at large, remain deeply split over the best way to leave the EU after more than four decades of membership.

By a vote of 245 to 218, the unelected upper chamber, the House of Lords, supported an amendment to her Brexit blueprint, the EU withdrawal bill, requiring ministers to negotiate continued membership of the European Economic Area, meaning that it would remain in the single market.

“The time has come over Brexit, really, for economic reality and common sense to prevail over political dogma and wishful thinking,” said Peter Mandelson, a member of the House of Lords from the main opposition Labour Party, who backed the amendment.

His comments drew criticism from pro-Brexit peers, including Conservative member Michael Forsyth who described the amendment as part of an attempt by “a number of people in this house who wish to reverse the decision of the British people”. Those proposing the amendment deny the charge.

This is the 13th time in recent weeks that the government has been defeated in the House of Lords on the draft legislation that will formally terminate Britain’s EU membership.

The house of Lords at the Houses of Parliament in London on October 31, 2017. (Dan Kitwood//AFP/Getty Images)

The votes can be overturned by the more powerful lower house, the House of Commons, where May’s party has a slim majority with the support of a small Northern Irish party, but could embolden lawmakers who hope to derail her plans to forge a new relationship with the EU.

The defeat was also damaging for the Labour leader Jeremy Corbyn after members of his party in the upper house defied orders to abstain from the vote and instead backed a cross-party alliance in support of the amendment.

While Corbyn has changed his position to support Britain’s membership of a customs union with the EU, he remains opposed to remaining in the single market.

No fixed Brexit date?

Earlier, opposition parties in the Lords and rebels in May’s Conservative Party inflicted another defeat on the government, voting to strip out the fixed timing for Britain to leave the EU at 11 p.m. on March 29 next year.

The government has already set the clock ticking in a two-year exit process hampered by her gamble on a snap election last June which cost her party its majority in parliament. It also remains unclear what the final divorce deal will look like.

Some lawmakers criticised the government’s plan to impose a specific date for Britain leaving the EU, saying it would create significant difficulties if negotiations with Brussels went down to the wire.

The Union Flag and a European Union flag fly near the Elizabeth Tower, housing the Big Ben bell in Parliament Square in central London, Britain September 9, 2017. (Reuters/Tolga Akmen)

The upper house of parliament also voted on Tuesday in favour of an amendment whereby Britain would continue to participate in EU agencies after leaving the bloc.

After the Lords, the bill will return to the House of Commons. Both houses have to agree on the final wording of the bill before it can become law.

This is the penultimate session for the bill in the upper chamber during the report stage, where members have already voted in favour of amendments including to compel ministers to seek a form of customs union with the EU.

May’s slim majority in the House of Commons is likely to be severely tested in the next few weeks when she is expected to urge her divided party to reject the proposed changes.

Lawmakers will have to decide later this year whether to back the government or reject the law — with the risk that Britain could crash out of the EU in 2019 with no deal in place.